4 Answers
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before you start shooting a scene/pose have someone hold the card in your primary light and hit it with your in camera meter. (in spot meetering mode, ideally with the card fully filling your spot meter area, even if that means zooming in.) set your exposure such that that is "properly exposed". Now remove the card and shoot away. Your main light source should be properly exposing subjects.

first shot of a session (or anytime you change the lighting substantially) slip the grey card into the shot in the main key light. Take a "throw away" shot with the card in it. If you have multiple light sources with radically different color temperatures, you'll want to shoot one with the grey card illuminated by each light source. When you're editing, use the grey cards in those shots to get your white balance adjustments, then mass apply them to the entire shoot.

There is also the "historical" use with dark room printing... shoot a frame with the card in it, even if it's way off to the side out of crop, then in the enlarger, slide the film so that you can print that bit, do a test strip of the card, develop, match the box on the test strip to your grey card to get the initial printing time for the negative.

/me wanders off to FIND my old dektol stained gray card... been using a modern white/grey/black target with digital lately... not sure where it is. ;)

Using a gray card, or even a color checking card or something like the X-Rite ColorChecker Passport, is pretty easy. Here are a few steps:

Set up your scene, whatever it is, be it landscape, portrait, or still life.

Place your gray card or color checking card in scene.

Have your subject hold it, clip it to a tripod, etc.

Set your white balance setting as appropriate for your lighting.

Use the closest fixed setting you can

Do not use AWB (automatic white balance) as that will produce inconsistent results

Snap a "calibration shot" of your scene.

Meter off the card

Now that you have a calibration shot, you can remove the gray card/color checker from your scene. Snap the rest of your shots for that particular lighting without the card in scene. It is important to note that, if for any reason, your lighting changes...you will need to take another calibration shot. Any change...this would include reorienting your camera or subject, changing the type of lighting, etc. Out in nature, changes caused by clouds obscuring sunlight would count as a change in lighting.

Once you have all of your shots, you actually CORRECT your white balance in post processing. The simplest way on earth to correct white balance with a gray card or color checker is with Adobe Lightroom. In develop mode, there is an extremely handy little tool...a dropper tool (color picker tool) right next to the white balance sliders. Click this, then click on your gray card in the first shot. Lightroom will automatically correct your white balance for you based on the 18% reflectance emitted by the gray card (the ideal tone to balance color from.) If you used something like X-Rite's ColorChecker Passport, there are several warming/cooling "swatches" that you an pick from. The nice thing about these kind of swatches is you have the option of warming or cooling your picture as you see fit in a color-accurate way.

If you do not have Lightroom, but do have Photoshop, you can use a similar approach. In the Levels tool, click the "Set Gray Point" dropper tool, and pick the gray card. Photoshop should make the same kind of adjustment as Lightroom. With Photoshop, unlike lightroom, you need to make sure that you pick the right dropper tool to correct color automatically, and you will only be able to use an actual gray card or white card, and use the matching "Set XYZ Point" option. Once you have set your color balance, save the current levels settings.

The final step to setting correct white balance for all of your images is to apply the current settings for your calibration image to the rest of your images for that lighting. In lightroom, this is again rediculously simple. Simply copy the white balance setting (CTRL+SHIFT+C, Uncheck All, Check "White Balance"), select all your other photos for that lighting, and paste (CTRL+SHIFT+V).

With Photoshop, it is a little more complex. You need to open the Levels tool for each image, and load the previously saved levels settings. I don't know of any batch way to do this in Photoshop, so it is rather time consuming if you have a lot of shots. Best to work your way through your shoot first, find and flag the keepers, and only work them.

Oh, forgot another option. Not quite as accurate, but an option if you don't have a tool that will let you set perfectly correct WB in post processing. Most cameras these days have a custom white balance setting. These are easy enough to set. Follow the four steps above, only in step 3, DO use AWB (auto white balance). Make the card cover as much of the scene as possible, illuminated by the same light as the rest of the scene. Once you have your shot, use the Custom WB tool, pick the image with the gray card, and set WB from that image. This will only really work with an actual gray card, a color checker card will not really produce the best results if you use Custom WB.

In addition to proper exposure (from the grey card) and post-processing colour correction (from a throw-away shot and white balance correction on your computer), some (most? all?) digital cameras also have a Custom White Balance setting. This is especially useful if you shoot JPEG and your images are under a common light source. (With RAW you can do it all in post, but JPEGs you'll get slightly better colour accuracy doing it on-camera).

You take a shot where some portion of the image is covered by the grey card (typically the centre region, perhaps 1/4 of the image area), making sure it's properly exposed and that the grey card is being lit by the light sources you're trying to account for.

Your camera will have an option to set the Custom White Balance based on an image (probably in the menu somewhere) which lets you configure the white balance that it will apply. You go into this menu option and select the photo you just took as the source for the custom white balance.

Set your white balance mode to Custom WB and it will apply the measured white balance (from that photo) to photos you take in this mode.

It's probably most useful if your lighting is constant, or if you're shooting with one particularly difficult light source (e.g. you can use Auto or a standard white balance on some photos, and the Custom WB on those under the particular light source).

If you've got a bunch of different lighting sources, or a combination of two (so you get variations as you move around) you might be best shooting RAW and taking a few different shots of the grey card and applying the most appropriate WB correction in post processing.

For exposure, put a gray card out in the scene you want to expose and then spot meter off of it. Spot metering either automatically sets your exposure based on the tonality of the grey card when you're not in manual, or you manually adjust your shutter speed and aperture until your in camera exposure meter reads a "correct" exposure. (Typically a little bar with the middle being "correct").

For post processing color correction, take a picture of your color card at the start of a session (or when lights drastically change) and then you have a 18% gray you can use to set all the "correct" colors during post processing.